pprehension of series as such. Under these
conditions the number technique becomes elaborate and requires time
and instruction for its mastery. The advance which mathematics has
made within a brief historical time is strikingly illustrated by the
words with which the celebrated mathematician, Sir Henry Savile, who
died in 1662, closed his career as a professor at Oxford:

By the grace of God, gentlemen hearers, I have performed
my promise. I have redeemed my pledge. I have explained,
according to my ability, the definitions, postulates, axioms,
and the first eight propositions of the _Elements_ of Euclid.
Here, sinking under the weight of years, I lay down my art and
my instruments.[260]

From the standpoint of modern mathematics, Sir Henry Savile and the
Bushman are both woefully backward; and in both cases the backwardness
is not a matter of mental incapacity, but of the state of the science.

In respect, then, to brain structure and the more important mental
faculties we find that no race is radically unlike the others. Still,
it might happen that the mental activities and products of two groups
were so different as to place them in different classes. But precisely
the contrary is true. There is in force a principle called the law of
parallelism in development, according to which any group takes much
the same steps in development as any other. The group may be belated,
indeed, and not reach certain stages, but the ground patterns of
life are the same in the lower races and in the higher. Mechanical
inventions, textile industries, rude painting, poetry, sculpture, and
song, marriage and family life, organization under leaders, belief
in spirits, a mythology, and some form of church and state exist
universally. At one time students of mankind, when they found a myth
in Hawaii corresponding to the Greek story of Orpheus and Eurydice, or
an Aztec poem of tender longing in absence, or a story of the deluge,
were wont to conjecture how these could have been carried over from
Greek or Elizabethan or Hebraic sources, or whether they did not
afford evidence of a time when all branches of the human race dwelt
together with a common fund of sentiment and tradition. But this
standpoint has been abandoned, and it is recognized that the human
mind and the outside world are essentially alike the world over; that
the mind everywhere acts on the same principles; and that, ignoring
the local, incidental, and